3D Display Methods in Computer Graphics: Parallel vs Perspective Projection
3
D
d
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By
Miss. T. Sarah Jeba Jency, M.Sc., M.Phil., B.Ed.,
U
N
I
T
–
4
C
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V
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a
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i
o
n
W
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a
t
i
s
3
d
d
i
s
p
l
a
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m
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i
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i
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?
3D
computer graphics
(
in
contrast to
2D
computer
graphic
s)
are graphics
that
utilize
a
three
dimensional
representation
of
geometric
data
that is
stored
in
the
computer
for
the
purposes of
performing
calculations and
rendering 2D images. Such images
may
be
for
later display
or
for
real-time
viewing
. We are
talk about the followings.
•
Parallel
Projection.
•
Perspective
Projection.
•
Depth
Cueing
Parallel
Projection:
A
parallel projection is a projection
of
an object in three-dimensional space onto a fixed plane,
known
as
the
projection plane or image plane,
where
the
rays,
known
as lines
of
sight or projection
lines, are parallel
to
each
other.
In
parallel projection,
z
co-ordinate is discarded and parallel,
lines
from
each vertex on
the
object are
extended
until they
intersect
the
view
plane.
We
connect
the
projected vertices
by line
segments which
correspond
to
connections on
the
original object. As
shown
in
next slide a parallel projection preserves relative proportions of
objects
but does not
produce
the
realistic
views.
Notes:
•
Project
points on
the
object
surface
along
parallel
lines
onto
the
display
plane.
•
Parallel
lines
are still parallel after
projection.
•
Used
in engineering and
architectural
drawings.
•
Views maintain
relative
proportions
of
the
object.
P
e
r
s
p
e
c
t
i
v
e
P
r
o
j
e
c
t
i
o
n
:
The
perspective projection,
on
the
other
hand,
produces
realistic views
but
does not
preserve relative proportions.
In
perspective
projection,
the lines of
projection are
not
parallel. Instead
,
they all
converge at
a
single
point
called
the
‘
center
of
projection
’
or
‘
projection
reference
point
’.
The
perspective projection
is perhaps
the
most
common
projection
technique familiar
to
us as
image
formed
by eye
or lenses of
photographic film
on
perspective
projection.
The
distance
and angles
are
not preserved
and
parallel
lines do not remain
parallel.
Instead,
they
all
converge
at
a
single
point
called
center of projection
or
projection
reference point
.
There are
3 types
of
perspective
projections:-
•
One point
perspective projection
is
simple
to
draw.
•
Two
point
perspective projection
gives
better
impression of
depth.
•
Three point
perspective projection
is
most
difficult
to
draw.
P
r
o
j
e
c
t
i
o
n
r
e
f
e
r
e
n
c
e
p
o
i
n
t
:
The
perspective projection
conveys
depth
information
by
making
distance
object
smalls
than
near
one.
This
is the
way
that
our
eyes
and a
camera
lens
form
images
and
so
the
displays are more
realistic.
The
disadvantage
is
that
if
object
have
only limited
variation
, the
image
may
not
provide
adequate depth
information
and
ambiguity
appears.
S
o
m
e
p
o
i
n
t
s
a
b
o
u
t
P
e
r
s
p
e
c
t
i
v
e
P
r
o
j
e
c
t
i
o
n
:
D
e
p
t
h
C
u
e
i
n
g
:
Depth cueing is implemented by
having
objects blend
into
the
background
color
with
increasing distance
from
the
viewer.
The
range
of
distances
over
which this
blending
occurs
is
controlled
by
the
sliders.
To
create
realistic image,
the
depth
information
is important so that
we
can
easily
identify, for
a
particular viewing direction,
which
is
the
front
and
which
is
the back
of
displayed
objects. The depth
of
an
object
can
be
represented
by
the
intensity
of
the
image.
The
parts
of
the
objects
closest
to
the
viewing position
are displayed
with the highest intensities
and
objects farther
away
are displayed
with decreasing
intensities.
This
effect
is
known as
‘depth
cueing’
.
Note:
•
To
easily identify
the
front
and
back of
display
objects.
•
Depth
information
can
be
included
using
various
methods.
•
A
simple method
to
vary
the
intensity
of objects according
to
their
distance
from
the
viewing
position.
•
Eg:
lines closest
to
the
viewing position
are displayed
with
the higher
intensities
and
lines farther
away
are displayed
with
lower
intensities.
Visible
line
and
surface
identification
I.
When
we
view
a
picture
containing
non-transparent
objects
and
surfaces,
then
we
cannot
see
those objects
from
view
which
are
behind
from
objects
closer
to
eye.
II.
We
must
remove
these
hidden
surfaces
to
get
a
realistic
screen
image.
The
identification
and
removal
of
these
surfaces
is
called
Hidden-surface
problem
Removing
hidden
surface
problem
Object-Space
method
Image-space
method
D
e
p
t
h
B
u
f
f
e
r
Z
−
B
u
f
f
e
r
M
e
t
h
o
d
0≤
depth
≤1
It
is an image-space approach.
The
basic idea is
to test the Z-depth of
each surface
to
determine
the
closest
visible
surface.
To
override
the
closer
polygons
from
the
far
ones,
two
buffers
named
frame
buffer
and
depth
buffer,
are
used.
D
e
p
t
h
b
u
f
f
e
r
i
s
u
s
e
d
t
o
s
t
o
r
e
d
e
p
t
h
v
a
l
u
e
s
f
o
r
x
,
y
p
o
s
i
t
i
o
n
,
a
s
s
u
r
f
a
c
e
s
a
r
e
p
r
o
c
e
s
s
e
d
0≤
depth
≤1
T
h
e
f
r
a
m
e
b
u
f
f
e
r
i
s
u
s
e
d
t
o
s
t
o
r
e
t
h
e
i
n
t
e
n
s
i
t
y
v
a
l
u
e
o
f
c
o
l
o
r
v
a
l
u
e
a
t
e
a
c
h
p
o
s
i
t
i
o
n
x
,
y
Scan-Line
Method:
The
Edge
Table
−
It
contains
coordinate endpoints
of
each
line
in
the
scene,
the
inverse
slope
of
each
line,
and
pointers
into
the
polygon
table
to
connect
edges
to
surfaces.
The
Polygon
Table
−
It
contains
the
plane
coefficients, surface
material
properties,
other
surface
data,
and
may
be
pointers
to
the edge
table.
Area-Subdivision
Method:
A.
Surrounding
surface
−
One
that
completely
encloses
the
area.
B.
Overlapping
surface
−
One
that
is
partly
inside
and
partly
outside
the
area.
C.
Inside
surface
−
One
that
is
completely
inside
the
area.
D.
Outside
surface
−
One
that
is
completely
outside
the
area.
A-Buffer
Method:
The
A-buffer
expands
on
the
depth
buffer
method
to
allow
transparencies.
The
key
data
structure
in
the
A-buffer
is
the
accumulation
buffer.
Each
position
in
the
A-buffer
has
two
fields
−
Depth
field
−
It
stores
a
positive
or
negative
real
number
Intensity
field
−
It
stores
surface-intensity
information
or
a
pointer
value
If
depth
>=
0,
the
number
stored
at
that
position
is
the
depth
of
a
single surface
overlapping the
corresponding
pixel
area.
The
intensity
field
then
stores
the
RGB
components
of the
surface
color
at
that
point
and
the
percent
of
pixel
coverage.
If
depth
<
0,
it
indicates
multiple-surface
contributions
to
the
pixel
intensity.
The
intensity
field
then
stores
a
pointer
to
a
linked
list
of
surface
data.
The
surface
buffer
in
the
A-buffer
includes
−
RGB
intensity
components
Opacity
Parameter
Depth
Percent
of
area
coverage
Surface
identifier
Surface
Rendering:
S
u
r
f
a
c
e
r
e
n
d
e
r
i
n
g
i
n
v
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.
Set
the
surface
intensity
of
objects
accordingto
Lighting
conditions
in
the
scene
Assigned
surface
characteristics
Lighting
specifications
include
the
intensity
and
positions
of
light
sources
and
the
general
background
illumination
required
for
ascene.
Surface
properties
include
degree
of
transparencyand
how
rough
or
smooth
of
the
surfaces
3D computer graphics utilize a three-dimensional representation for rendering images. This article discusses parallel and perspective projection methods, highlighting their differences in preserving proportions and creating realistic views. Parallel projection maintains relative proportions, while perspective projection provides depth perception but may introduce ambiguity. Depth cueing and different types of perspective projections are also explored.
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Presentation Transcript
UNIT 4 Computer Graphics and Visualization 3D display methods in Computer Graphics By Miss. T. Sarah Jeba Jency, M.Sc., M.Phil., B.Ed.,
What is 3d display methods in computer graphics? 3D computer graphics (in contrast to 2D computer graphics) are graphics that utilize a three dimensional representation of geometric data that is stored in the computer for the purposes of performing rendering 2D images. Such images may be for later display or for real-time viewing. We are talk about the followings. calculations and Parallel Projection. Perspective Projection. Depth Cueing
Parallel Projection: A parallel projection is a projection of an object in three-dimensional space onto a fixed plane, known as the projection plane or image plane, where the rays, known as lines of sight or projection lines, are parallel to each other. We connect the projected vertices by line correspond to connections on the original object. As shown in next slide a parallel projection preserves relative proportions of objects but does not produce the realistic views. segments which In parallel projection, z co-ordinate is discarded and parallel, lines from each vertex on the object intersect the view plane. are extended until they Notes: Project points on the object surface along parallel lines onto the display plane. Parallel lines are still parallel after projection. Used in engineering and architectural drawings. Views maintain relative proportions of the object.
Perspective Projection : The perspective projection, on the other hand, produces realistic views but does not preserve relative proportions. In perspective projection, the lines of projection are not parallel. Instead , they all converge at a single point called the center of projection or projection reference point . The perspective projection is perhaps the most common projection technique familiar to us as image formed by eye or lenses of photographicfilm on perspective projection.
Projection reference point : The distance and angles are not preserved and parallel lines do not remain parallel. Instead, they all converge at a single point called center of projection or projection reference point. There are 3 types ofperspective projections:- One point perspective projection is simple to draw. Two point perspective projection gives better impression of depth. Three point perspective projection is most difficult to draw. Some points about Perspective Projection : The perspective projection conveys depth information by making distance object smalls than near one. This is the way that our eyes and a camera lens form images and so the displays are more realistic. The disadvantage is that if object have only limited variation , the image may not provide adequate depth information and ambiguity appears.
Depth Cueing : Depth cueing is implemented by having background color with increasing distance from the viewer. The range of distances over which this blending occurs is controlled by the sliders. objects blend into the Tocreate realistic image, the depth information is important so that we can easily identify, for a particular viewing direction, which is the front and which is the back of displayed objects. The depth of an object can be represented by the intensity of the image. The parts of the objects closest to the viewing position are displayed with the highest intensities and objects farther away are displayed with decreasing intensities. This effect is known as depth cueing . Note: To easily identify the front and back of display objects. Depth information can be included using various methods. A simple method to vary the intensity of objects according to their distance from the viewingposition. Eg: lines closest to the viewing position are displayed with the higher intensities and lines farther away are displayed with lower intensities.
Visiblelineand surfaceidentification When we view a picture containing non-transparent objects and surfaces, then we cannot see those objects from view which are behind from objects closer to eye. I. We must remove these hidden surfaces to get a realistic screen image. The identification and removal of these surfaces is called Hidden-surface problem II. Removing hidden surface problem Object-Space method Image-space method
0depth1 Depth Buffer Z Buffer Method It is an image-space approach. The basic idea is to test the Z-depth of each surface to determine the closest visible surface. To override the closer polygons from the far ones, two buffers named frame buffer and depth buffer, are used. Depth buffer is used to store depth values for x,y position, as surfaces are processed 0 depth 1 The frame buffer is used to store the intensity value of color value at each position x,y
Scan-Line Method: The Edge Table It contains coordinate endpoints of each line in the scene, the inverse slope of each line, and pointers into the polygon table to connect edges to surfaces. The Polygon Table It contains the plane coefficients, surface material properties, other surface data, and may be pointers to the edge table.
Area-Subdivision Method: Surrounding surface One that completely encloses thearea. A. Overlapping surface One that is partly inside and partly outside the area. B. Inside surface One that is completely inside the area. C. Outside surface One that is completely outside thearea. D.
A-Buffer Method: The A-buffer expands on the depth buffer method to allow transparencies. The key data structure in the A-buffer is the accumulation buffer. Each position in the A-buffer has two fields Depth field It stores a positive or negative realnumber Intensity field It stores surface-intensity information or a pointer value If depth >= 0, the number stored at that position is the depth of a single surface overlapping the corresponding pixel area. The intensity field then stores the RGB components of the surface color at that point and the percent of pixel coverage.
If depth < 0, it indicates multiple-surface contributions to the pixel intensity. The intensity fieldthen stores a pointer to a linked list of surface data. The surface buffer in the A-buffer includes RGB intensity components OpacityParameter Depth Percent of areacoverage Surfaceidentifier
Surface Rendering: Surface rendering involves setting the surface intensity of objects according to the lighting conditions in the scene and according to assigned surface characteristics. The lighting conditions specify the intensity and positions of light sources and the general background illumination requiredforascene. On the other hand the surface characteristics of objects specify the degree of transparency and smoothnessor roughnessof the surface;usuallythe surfacerenderingmethodsare combinedwith perspective and visible surface identification to generate a high degree of realism in a displayed scene. Setthe surfaceintensity of objectsaccordingto Lightingconditions in thescene Assignedsurfacecharacteristics Lighting specificationsinclude the intensity andpositions of light sources and the general background illumination required for ascene. Surface properties include degree oftransparencyand how roughor smoothof thesurfaces
